An Acoustic Model for Wave Propagation in a Weak Layer

An acoustic model is developed for transient wave propagation in a weak layer excited by prescribed pressure or prescribed acceleration at the boundary. The validity of the acoustic model is investigated for the two excitations. A comparison of transient response from the acoustic model and a 3D axisymmetric elastic model reveals that for prescribed acceleration the acoustic model fails to capture important features of the elastic model even as Poisson ratio $ν$ approaches $1∕2$⁠. However for prescribed pressure, the two models agree since shear stress is reduced. For prescribed acceleration adopting the modal approach, the mixed boundary-value problem on the excited boundary is converted to a pure traction problem utilizing the influence method. To validate the elaborate modal approach a finite difference model is also developed.